Surely a rainbow is one of the most beautiful, if not the most
beautiful, phenomenon of nature. It is also such an unexpected
phenomenon. Although most humans have seen simple rainbows many
times there are a number of more complex versions of rainbows that
few have experienced.

A rainbow occurs because light rays enter water droplets and are
refracted and reflected out at a different angle. This refractive
angle, the difference in angle between the ray entering the ray leaving
determines the angle in the sky at which the rainbow is observed, as
is shown in the diagram below.

The determination of the refractive angles for rainbows is dealt with
elsewhere.

A simple rainbow, called a primary rainbow, is one for which
the refractive angle is about 42°. It is of the form shown
below with red appearing at the top and blue indigo appearing at the
bottom.

The primary rainbow and the refractive angle of 42° are associated
with a light ray having one reflection before leaving the droplet. When
there are two reflections the rainbow is called secondary. The refractive
angle is about 50° The image
below depicts the case of a primary and secondary rainbow appearing.
The order of the colors in a secondary rainbow are the reverse of the
order in the primary rainbow.

When there is a large body of water near the site of a rainbow the
sun's rays may be reflected off the water and enter the water droplets
from below. This results in a rainbow positioned differently from the
unreflected rainbows. There may be a primary reflected rainbow in
addition to the primary and secondary rainbows, as shown below.

Or, there may be both a primary and secondary reflected rainbow as
shown below.

There may be three reflection of a light ray in a rain droplet
before it leaves the droplet. The resulting rainbow is called a
tertiary rainbow. Its refractive angle is about 172° and it is
difficult to display it along with the primary and secondary rainbows.